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# A SONAR uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR, the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s.

Q 2.30: A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR, the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = $1450\ m s^{-1}$).

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Given,

77.0 s is the total time between the generation of a probe wave and the reception of its echo after reflection.

$\therefore$ Time taken by sound to reach the enemy submarine = Half of the total time = $\frac{1}{2}\times 77 s = 38.5 s$

The distance of enemy ship = Speed of sound x Time taken to reach the submarine

$1450\ ms^{-1} \times 38.5\ s = 55825\ m = 55.8\ km$

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